Sharp lower bounds involving circuit layout system

Abstract

The circuit layout system CLS{ n (A), N (A * ), δ} E in a Euclidean space E is defined. By means of algebraic, analytic, geometric and inequality theories, we obtain several sharp lower bounds involving the circuit layout system. MSC: 51K05; 26D15

Sharp upper bound involving circuit layout system

“…. , A * N such that the total length 1 2 In order to study the above problem, we need to recall some basic concepts [2,6,7]. Let E be a Euclidean space, and let α, β ∈ E. The inner product of α and β is denoted by α, β and the norm of α is denoted by α √ α 2 , where α 2 α, α .…”

A Brunn-Minkowski-type inequality involving γ -mean variance and its applications

“…In [8,17], the authors obtained the following Minkowski-type inequality: Let A ∈ R n×n . If A T = A, A 0, then for any x, y ∈ R n , we have…”

“…We say that f Varf is a semi-norm of the function f . Brunn-Minkowski-type inequality has a wide range of applications, especially in probability and statistics, algebraic geometry, and space science (see [3,4,7,8,14,17,19]). …”